The "conservative" National Review went back to every Supreme Court appointment in history and made charts showing exactly what happened to answer your question. The New York Times, with its "moral clarity" performed no such analysis and presented no such charts.
Why put ‘conservative’ in quotes? If you Google the name of the magazine their own meta description says conservative as the second word, so they consider themselves a partisan source.
In English quotes can be ambiguous, in this case they mean it is a direct quote from the parent comment (for emphasis, basically), not that it's under suspicion.
It's amazing how if someone shared NYTimes, WaPo, VOX, VICE etc, then everyone's cool. But if someone shares a slightly right leaning source, people start asking for "non-conservative" source.
Honestly you won't get a clear picture from reading a single source, or even multiple sources that lean a particular way. You have to read multiple sources from both political leanings.
Think of it as a trial. Liberal leaning media is the prosecutor and conservative media is the defendant. Depending on the topic, these roles are reversed.